Computer Science ›› 2026, Vol. 53 ›› Issue (3): 115-128.doi: 10.11896/jsjkx.250200118

• Database & Big Data & Data Science • Previous Articles     Next Articles

Review of Methods and Applications of Graph Diffusion Models

ZHAO Haihua1, TANG Rui2, MO Xian1   

  1. 1 College of Information Engineering, Ningxia University, Yinchuan 750021, China
    2 College of Cyberspace Security, Sichuan University, Chengdu 610207, China
  • Received:2025-02-27 Revised:2025-05-29 Published:2026-03-12
  • About author:ZHAO Haihua,born in 1999,postgra-duate,is a member of CCF(No.U6274G).His main research interests include graph learning and recommender systems.
    MO Xian,born in 1990,Ph.D,associate professor,master supervisor,is a member of CCF(No.R6178M).His main research interests include graph learning,network representation learning and recommender system.
  • Supported by:
    Natural Science Foundation of Ningxia(2024AAC05011),National Natural Science Foundation of China(62306157,62202320) and Key Research and Development Program of Ningxia(Special Program for Recruiting High-Caliber Talent)(2025BEH04048).

Abstract: Graph diffusion models,as an emerging paradigm in deep generative modeling,have demonstrated remarkable advantages in modeling complex graph-structured data due to their progressive generation mechanisms and structural flexibility.This paper systematically reviews the methodological evolution and application advancements of graph diffusion models.Firstly,three core paradigms are analyzed from the perspective of generative mechanisms:denoising diffusion probabilistic models,score-based diffusion generative models,and stochastic differential equation(SDE)-based diffusion generative models.Subsequently,to address the high-dimensional,discrete,and non-Euclidean nature of graph data,innovative technical breakthroughs of these three fundamental diffusion models in graph data processing are categorized,summarized,and subjected to in-depth analysis.Building on this foundation,the evaluation frameworks for graph diffusion models are systematically summarized and analyzed.At the application level,the study focuses on the applications of graph diffusion models in recommendation systems and molecular modeling.Finally,based on the above discussions,prospects for future challenges and potential research directions are proposed,encompassing four aspects:the discrete nature of graph data,conditional generation of graph diffusion models,application expansion,and evaluation frameworks.

Key words: Graph diffusion models, Diffusion model, Graph generation, Recommendation systems, Molecular modeling

CLC Number: 

  • TP183
[1]YANG Q,LI P,XU X,et al.A comparative study on enhancing prediction in social network advertisement through data augmentation[C]//2024 4th International Conference on Machine Learning and Intelligent Systems Engineering(MLISE).IEEE,2024:214-218.
[2]FAN W Q,DERR T,MA Y,et al.Deep adversarial social re-commendation[C]//Proceedings of the 28th International Joint Conference on Artificial Intelligence.AAAI,2019:1351-1357.
[3]GHOSH A,MITRA S,LAN A.Dips:differentiable policy forsketching in recommender systems[C]//Proceedings of the AAAI Conference on Artificial Intelligence.2022:6703-6712.
[4]LUO H,MENG X,WANG S,et al.Spectral-based graph neural networks for complementary item recommendation[C]//Proceedings of the AAAI Conference on Artificial Intelligence.2024:8868-8876.
[5]XU M,POWERS A S,DROR R O,et al.Geometric latent diffusion models for 3d molecule generation[C]//International Conference on Machine Learning.PMLR,2023:38592-38610.
[6]HUANG L,XU T,YU Y,et al.A dual diffusion model enables 3D molecule generation and lead optimization based on target pockets[J].Nature Communications,2024,15(1):2657.
[7]KIPF T N,WELLING M.Semi-supervised classification withgraph convolutional networks[C]//International Conference on Learning Representations.2017.
[8]HAMILTON W,YING Z,LESKOVEC J.Inductive representation learning on large graphs[C]//Advances in Neural Information Processing Systems.2017:1025-1035.
[9]AMIT T,SHAHARBANY T,NACHMANI E,et al.Segdiff:Image segmentation with diffusion probabilistic models[C]//Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition.2018.
[10]HO J,SAHARIA C,CHAN W,et al.Cascaded diffusion models for high fidelity image generation[J].Journal of Machine Learning Research.2022,23(47):1-33.
[11]GAO Z,GUO J,TAN X,et al.Difformer:Empowering diffusion models on the embedding space for text generation[C]//Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics.2024:4664-4683.
[12]GONG S,LI M,FENG J,et al.Diffuseq:Sequence to sequence text generation with diffusion models[C]//International Conference on Learning Representations.2023.
[13]TASHIRO Y,SONG J,SONG Y,et al.CSDI:Conditional score-based diffusion models for probabilistic time series imputation[J].Advances in Neural Information Processing Systems,2021,34:24804-24816.
[14]ALCARAZ J M L,STRODTHOFF N.Diffusion-based time series imputation and forecasting with structured state space mo-dels[J].arXiv:2208.09399,2022.
[15]JIANG Y,YANG Y,XIA L,et al.Diffkg:Knowledge graph diffusion model for recommendation[C]//Proceedings of the 17th ACM International Conference on Web Search and Data Mi-ning.2024:313-321.
[16]WU L,GONG C,LIU X,et al.Diffusion-based molecule generation with informative prior bridges[J].Advances in Neural Information Processing Systems,2022,35:36533-36545.
[17]KINGMA D P,WELLING M.Auto-encoding variational Bayes[J].arXiv:1312.6114,2013.
[18]KIPF T N,WELLING M.Variational graph auto-encoders[J].arXiv:1611.07308,2016.
[19]SIMONOVSKY M,KOMODAKIS N.GraphVAE:Towardsgeneration of small graphs using variational autoencoders[C]//Artificial Neural Networks and Machine Learning-ICANN 2018:27th International Conference on Artificial Neural Networks.Springer,2018:412-422.
[20]LIU Q,ALLAMANIS M,BROCKSCHMIDT M,et al.Con-strained graph variational autoencoders for molecule design[C]//Proceedings of the 32nd International Conference on Neural Information Processing Systems.Curran Associates Inc.,2018:7806-7815.
[21]GOODFELLOW I,POUGET-ABADIE J,MIRZA M,et al.Ge-nerative adversarial networks[J].Communications of the ACM,2020,63(11):139-144.
[22]DE CAO N,KIPF T.MolGAN:An implicit generative model for small molecular graphs[J].arXiv:1805.11973,2018.
[23]YANG C,ZHUANG P,SHI W,et al.Conditional structure ge-neration through graph variational generative adversarial nets[C]//Conference on Neural Information Processing Systems.2019:1338-1349.
[24]REZENDE D,MOHAMED S.Variational inference with nor-malizing flows[C]//International Conference on Machine Learning.PMLR,2015:1530-1538.
[25]ZANG C,WANG F.Moflow:an invertible flow model for gener-ating molecular graphs[C]//Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining.2020:617-626.
[26]LUO Y,YAN K,JI S.Graphdf:A discrete flow model for molecular graph generation[C]//International Conference on Machine Learning.PMLR,2021:7192-7203.
[27]LIU J,KUMAR A,BA J,et al.Graph normalizing flows[C]//Proceedings of the 33rd International Conference on Neural Information Processing Systems.Red Hook,NY:Curran Associates Inc.,2019:13578-13588.
[28]YOU J,YING R,REN X,et al.Graphrnn:Generating realistic graphs with deep auto-regressive models[C]//International Conference on Machine Learning.PMLR,2018:5708-5717.
[29]POPOVA M,SHVETS M,OLIVA J,et al.MolecularRNN:Generating realistic molecular graphs with optimized properties[J].arXiv:1905.13372,2019.
[30]HO J,JAIN A,ABBEEL P.Denoising diffusion probabilisticmodels[J].Advances in Neural Information Processing Systems,2020,33:6840-6851.
[31]NICHOL A Q,DHARIWAL P.Improved denoising diffusion probabilistic models[C]//International Conference on Machine Learning.PMLR,2021:8162-8171.
[32]SOHL-DICKSTEIN J,WEISS E,MAHESWARANATHANN,et al.Deep unsupervised learning using nonequilibrium thermodynamics[C]//International Conference on Machine Lear-ning.PMLR,2015:2256-2265.
[33]SONG Y,ERMON S.Generative modeling by estimating gradients of the data distribution[C]//Proceedings of the 33rd International Conference on Neural Information Processing Systems.Red Hook,NY:Curran Associates Inc.,2019:11918-11930.
[34]SONG Y,ERMON S.Improved techniques for training score-based generative models[J].Advances in Neural Information Processing Systems,2020,33:12438-12448.
[35]SONG Y,DURKAN C,MURRAY I,et al.Maximum likelihood training of score-based diffusion models[J].Advances in Neural Information Processing Systems.2021,34:1415-1428.
[36]SONG Y,SOHL-DICKSTEIN J,KINGMA D P,et al.Score-based generative modeling through stochastic differential equations[C]//International Conference on Learning Representations.2020.
[37]RONNEBERGER O,FISCHER P,BROX T.U-net:Convolu-tional networks for biomedical image segmentation[C]//18th International Conference Medical Image Computing and Computer-Assisted Intervention(MICCAI 2015).Springer,2015:234-241.
[38]WELLING M,THE Y W.Bayesian learning via stochastic gradient Langevin dynamics[C]//Proceedings of the 28th International Conference on Machine Learning.2011:681-688.
[39]HAEFELI K K,MARTINKUS K,PERRAUDIN N,et al.Diffusion models for graphs benefit from discrete state spaces[J].arXiv:2210.01549,2022.
[40]VIGNAC C,KRAWCZUK I,SIRAUDIN A,et al.Digress:Discrete denoising diffusion for graph generation[C]//International Conference on Learning Representations.2023.
[41]CHEN X,HE J,HAN X,et al.Efficient and degree-guidedgraph generation via discrete diffusion modeling[C]//Procee-dings of the 40th International Conference on Machine Lear-ning.2023:4585-4610.
[42]WU M,CHEN X,LIU L.EDGE++:Improved Training and Sampling of EDGE[J].arXiv:2310.14441,2023.
[43]GROVER A,ZWEIG A,ERMON S.Graphite:Iterative generative modeling of graphs[C]//International Conference on Machine Learning.PMLR,2019:2434-2444.
[44]NIU C,SONG Y,SONG J,et al.Permutation invariant graphgeneration via score-based generative modeling[C]//International Conference on Artificial Intelligence and Statistics.PMLR,2020:4474-4484.
[45]JO J,KIM D,HWANG S J.Graph generation with diffusion mixture[C]//International Conference on Machine Learning.2024.
[46]YANG L,ZHANG Z,ZHANG W,et al.Score-based graph ge-nerative modeling with self-guided latent diffusion[C]//International Conference on Learning Representations.2023.
[47]CHEN X,LI Y,ZHANG A,et al.Nvdiff:Graph generationthrough the diffusion of node vectors[J].arXiv:2211.10794,2022.
[48]JO J,LEE S,HWANG S J.Score-based generative modeling of graphs via the system of stochastic differential equations[C]//International Conference on Machine Learning.PMLR,2022:10362-10383.
[49]LUO T,MO Z,PAN S J.Fast graph generation via spectral diffusion[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2023,46(5):3496-3508.
[50]HUANG H,SUN L,DU B,et al.Graphgdp:Generative diffu-sion processes for permutation invariant graph generation[C]//2022 IEEE International Conference on Data Mining(ICDM).IEEE,2022:201-210.
[51]WEN L,TANG X,OUYANG M,et al.Hyperbolic Graph Diffusion Model[C]//Proceedings of the AAAI Conference on Artificial Intelligence.2024:15823-15831.
[52]SEN P,NAMATA G,BILGIC M,et al.Collective classification in network data[J].AI Magazine,2008,29(3):93-93.
[53]RAMAKRISHNAN R,DRAL P O,RUPP M,et al.Quantum chemistry structures and properties of 134 kilo molecules[J].Scientific Data,2014,1(1):1-7.
[54]IRWIN J J,STERLING T,MYSINGER M M,et al.ZINC:a free tool to discover chemistry for biology[J].Journal of Che-mical Information and Modeling,2012,52(7):1757-1768.
[55]GRETTON A,BORGWARDT K M,RASCH M J,et al.A kernel two-sample test[J].The Journal of Machine Learning Research,2012,13(1):723-773.
[56]LIU C C,CHAN H,LUK K,et al.Auto-regressive graph gene-ration modeling with improved evaluation methods[C]//Confe-rence on Neural Information Processing Systems.2019.
[57]XU K,HU W,LESKOVEC J,et al.How powerful are graphneural networks?[J].arXiv:1810.00826,2018.
[58]WALKER J,ZHONG T,ZHANG F,et al.Recommendation via collaborative diffusion generative model[C]//International Conference on Knowledge Science,Engineering and Management.Cham:Springer,2022:593-605.
[59]HOU Y,PARK J D,SHIN W Y.Collaborative Filtering Based on Diffusion Models:Unveiling the Potential of High-Order Connectivity[J].arXiv:2404.14240,2024.
[60]YI Z,WANG X,OUNIS I.A directional diffusion graph transformer for recommendation[J].arXiv:2404.03326,2024.
[61]LEE C,CHIO J,WI H,et al.Stochastic Sampling for Contrastive Views and Hard Negative Samples in Graph-based Collaborative Filtering[J].arXiv:2405.00287,2024.
[62]LONG J,YE G,CHEN T,et al.Diffusion-based cloud-edge-device collaborative learning for next POI recommendations[C]//Proceedings of the 30th ACM SIGKDD Conference on Know-ledge Discovery and Data Mining.2024:2026-2036.
[63]HUANG H,HUANG C,CHANG X,et al.Dual ConditionalDiffusion Models for Sequential Recommendation[J].arXiv:2410.21967,2024.
[64]WU Z,WANG X,CHEN H,et al.Diff4rec:Sequential recommendation with curriculum-scheduled diffusion augmentation[C]//Proceedings of the 31st ACM International Conference on Multimedia.2023:9329-9335.
[65]YANG Z,WU J,WANG Z,et al.Generate what you prefer:Reshaping sequential recommendation via guided diffusion[J].Advances in Neural Information Processing Systems,2023,36:24247-24261.
[66]YU P,TAN Z,LU G,et al.Ld4mrec:Simplifying and powering diffusion model for multimedia recommendation[J].arXiv:2309.15363,2023.
[67]JIANG Y,XIA L,WEI W,et al.Diffmm:Multi-modal diffusion model for recommendation[C]//Proceedings of the 32nd ACM International Conference on Multimedia.2024:7591-7599.
[68]MA H,YANG Y,MENG L,et al.Multimodal conditioned diffu-sion model for recommendation[C]//Companion Proceedings of the ACM Web Conference 2024.2024:1733-1740.
[69]SIMM G N C,HERNANDEZ-LOBATO J M.A generativemodel for molecular distance geometry[C]//Proceedings of the 37th International Conference on Machine Learning.PMLR,2020:8949-8958.
[70]XU M,LUO S,BENGIO Y,et al.Learning neural generativedynamics for molecular conformation generation[C]//International Conference on Learning Representations.2021.
[71]SHI C,LUO S,XU M,et al.Learning gradient fields for molecular conformation generation[C]//International Conference on Machine Learning.PMLR,2021:9558-9568.
[72]LUO S,SHI C,XU M,et al.Predicting molecular conformation via dynamic graph scorematching[J].Advances in Neural Information Processing Systems,2021,34:19784-19795.
[73]XU M,WANG W,LUO S,et al.An end-to-end framework for molecular conformation generation via bilevel programming[C]//International Conference on Machine Learning.PMLR,2021:11537-11547.
[74]XU M,YU L,SONG Y,et al.Geodiff:A geometric diffusion model for molecular conformation generation[J].arXiv:2203.02923,2022.
[75]HOOGEBOOM E,SATORRAS V G,VIGNAC C,et al.Equivariant diffusion for molecule generation in 3d[C]//International Conference on Machine Learning.PMLR,2022:8867-8887.
[76]BAO F,ZHAO M,HAO Z,et al.Equivariant energy-guided sde for inverse molecular design[J].arXiv:2209.15408,2022.
[77]JING B,GORSO G,CHANG J,et al.Torsional diffusion for molecular conformer generation[J].Advances in Neural Information Processing Systems,2022,35:24240-24253.
[78]HUANG L,ZHANG H,XU T,et al.Mdm:Molecular diffusion model for 3d molecule generation[C]//Proceedings of the AAAI Conference on Artificial Intelligence.2023:5105-5112.
[79]ANAND N,ACHIM T.Protein structure and sequence generation with equivariant denoising diffusion probabilistic models[J].arXiv:2205.15019,2022.
[80]MOHAMED A,OKHONKO D,ZETTLEMOYER L.Trans-formers with convolutional context for asr[J].arXiv:1904.11660,2019.
[81]WATSON J L,JUERGENS D,BENNETT N R,et al.De novo design of protein structure and function with RFdiffusion[J].Nature,2023,620(7976):1089-1100.
[82]BAEK M,DIMAIO F,ANISHCHENKO I,et al.Accurate prediction of protein structures and interactions using a three-track neural network[J].Science,2021,373(6557):871-876.
[83]LEE J S,KIM J,KIM P M.ProteinSGM:Score-based generative modeling for de novo protein design[J].bioRxiv:2022.07.13.499967,2022.
[84]TRIPPE B L,YIM J,TISCHER D,et al.Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem[J].arXiv:2206.04119,2022.
[85]WU K E,YANG K K,VAN DEN BERG R,et al.Protein structure generation via folding diffusion[J].Nature Communications,2024,15(1):1059.
[1] WANG Yiming, JIAO Min, ZHAO Suyun, CHEN Hong, LI Cuiping. Prompt-conditioned Representation Learning with Diffusion Models for Semi-supervised Clustering [J]. Computer Science, 2026, 53(3): 158-165.
[2] LUO Xuyang, TAN Zhiyi. Knowledge-aware Graph Refinement Network for Recommendation [J]. Computer Science, 2025, 52(7): 103-109.
[3] ZOU Rui, YANG Jian, ZHANG Kai. Low-resource Vietnamese Speech Synthesis Based on Phoneme Large Language Model andDiffusion Model [J]. Computer Science, 2025, 52(6A): 240700138-6.
[4] HOU Zhexiao, LI Bicheng, CAI Bingyan, XU Yifei. High Quality Image Generation Method Based on Improved Diffusion Model [J]. Computer Science, 2025, 52(6A): 240500094-9.
[5] KANG Kai, WANG Jiabao, XU Kun. Balancing Transferability and Imperceptibility for Adversarial Attacks [J]. Computer Science, 2025, 52(6): 381-389.
[6] GENG Sheng, DING Weiping, JU Hengrong, HUANG Jiashuang, JIANG Shu, WANG Haipeng. FDiff-Fusion:Medical Image Diffusion Fusion Network Segmentation Model Driven Based onFuzzy Logic [J]. Computer Science, 2025, 52(6): 274-285.
[7] YANG Lan, ZHAO Jinxiong, LI Zhiru, ZHANG Xun, DI Lei, CAI Yunjie, ZHANG Hehui. Few-shot Image Generative Adaptation for Power Defect Scenes [J]. Computer Science, 2025, 52(11A): 241100149-8.
[8] LI Sihui, CAI Guoyong, JIANG Hang, WEN Yimin. Novel Discrete Diffusion Text Generation Model with Convex Loss Function [J]. Computer Science, 2025, 52(10): 231-238.
[9] LIU Hui, JI Ke, CHEN Zhenxiang, SUN Runyuan, MA Kun, WU Jun. Malicious Attack Detection in Recommendation Systems Combining Graph Convolutional Neural Networks and Ensemble Methods [J]. Computer Science, 2024, 51(6A): 230700003-9.
[10] HUANG Feihu, LI Peidong, PENG Jian, DONG Shilei, ZHAO Honglei, SONG Weiping, LI Qiang. Multi-agent Based Bidding Strategy Model Considering Wind Power [J]. Computer Science, 2024, 51(6A): 230600179-8.
[11] HUANG Chungan, WANG Guiping, WU Bo, BAI Xin. Diversified Recommendation Based on Light Graph Convolution Networks and ImplicitFeedback Enhancement [J]. Computer Science, 2024, 51(6A): 230900038-11.
[12] GE Yinchi, ZHANG Hui, SUN Haohang. Differential Privacy Data Synthesis Method Based on Latent Diffusion Model [J]. Computer Science, 2024, 51(3): 30-38.
[13] ZHU Xudong, LAI Teng. Multimodal Contrastive Learning Based Scene Graph Generation [J]. Computer Science, 2024, 51(11A): 231200185-5.
[14] ZHOU Hao, LUO Tingjin, CUI Guoheng. Scene Graph Generation Combined with Object Attribute Recognition [J]. Computer Science, 2024, 51(11): 205-212.
[15] YAN Zhihao, ZHOU Zhangbing, LI Xiaocui. Survey on Generative Diffusion Model [J]. Computer Science, 2024, 51(1): 273-283.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!